Torque measurement at the single-molecule level

Optical Torque Calculations and Measurements for DNA Torsional Studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping, but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

SIGNIFICANCE

We developed a simulation platform based on the finite element method for force and torque calculation for particles in an angular optical trap (AOT), with considerations of tightly focused Gaussian beam, spherical aberrations, and optically anisotropic particles. Experimental measurements of focal shift ratio, force, and torque under multiple conditions were in good agreement with predictions from the simulations. We also demonstrated that intrinsic DNA torsional properties can be robustly measured under different AOT measurement conditions, strongly validating our simulations and calibrations. Our platform can facilitate trapping particle design for single-molecule assays using the AOT.

Reciprocating RNA Polymerase batters through roadblocks

RNA polymerases must transit through protein roadblocks to produce full-length transcripts. Here we report real-time measurements of Escherichia coli RNA polymerase passing through different barriers. As intuitively expected, assisting forces facilitated, and opposing forces hindered, RNA polymerase passage through lac repressor protein bound to natural binding sites. Force-dependent differences were significant at magnitudes as low as 0.2 pN and were abolished in the presence of the transcript cleavage factor GreA, which rescues backtracked RNA polymerase. In stark contrast, opposing forces promoted passage when the rate of RNA polymerase backtracking was comparable to, or faster than the rate of dissociation of the roadblock, particularly in the presence of GreA. Our experiments and simulations indicate that RNA polymerase may transit after roadblocks dissociate, or undergo cycles of backtracking, recovery, and ramming into roadblocks to pass through. We propose that such reciprocating motion also enables RNA polymerase to break protein-DNA contacts that hold RNA polymerase back during promoter escape and RNA chain elongation. This may facilitate productive transcription in vivo.

Alterations in the chromatin packaging, driven by transcriptional activity, revealed by AFM

BACKGROUND

The gene expression differs in the nuclei of normal and malignant mammalian cells, and transcription is a critical initial step, which defines the difference. The mechanical properties of transcriptionally active chromatin are still poorly understood. Recently we have probed transcriptionally active chromatin of the nuclei subjected to mechanical stress, by Atomic Force Microscopy (AFM) [1]. Nonetheless, a systematic study of the phenomenon is needed.

METHODS

Nuclei were deformed and studied by AFM. Non-deformed nuclei were studied by fluorescence confocal microscopy. Their transcriptional activity was studied by RNA electrophoresis.

RESULTS

The malignant nuclei under the study were stable to deformation and assembled of 100-300 nm beads-like units, while normal cell nuclei were prone to deformation. The difference in stability to deformation of the nuclei correlated with DNA supercoiling, and transcription-depended units were responsive to supercoils breakage. The inhibitors of the topoisomerases I and II disrupted supercoiling and made the malignant nucleus prone to deformation. Cell nuclei treatment with histone deacetylase inhibitors (HDACIs) preserved the mechanical stability of deformed malignant nuclei and, at the same time, made it possible to observe chromatin decondensation up to 20-60 nm units. The AFM results were supplemented with confocal microscopy and RNA electrophoresis data.

CONCLUSIONS

Self-assembly of transcriptionally active chromatin and its decondensation, driven by DNA supercoiling-dependent rigidity, was visualized by AFM in the mechanically deformed nuclei.

GENERAL SIGNIFICANCE

We demonstrated that supercoiled DNA defines the transcription mechanics, and hypothesized the nuclear mechanics in vivo should depend on the chromatin architecture.

Two Different Ways of Stress Release in Supercoiled DNA Minicircles under DNA Nick

It is generally believed that DNA nick is an effective way to release stress in supercoiled DNA, resulting from the twisting motion that individual strands rotate around the axis of the DNA helix. Here, we use MD simulations based on the oxDNA model to investigate the relaxation of 336 bp supercoiled minicircular DNA under DNA nick. Our simulations show that stress release, characterized by the abrupt decrease in linking number, may be induced by two types of DNA motion depending on the nick position. Except for the twisting motion, there is a writhing motion, that is, double strands collectively rotating with one plectoneme removal, which may occur in the process of DNA relaxation with the nick position in the loop region. Moreover, the writhing motion is more likely to occur in the DNA with relatively high hardness, such as C-G pairs. Our simulation results uncover the relationship between structural transformation, stress release, and DNA motion during the dynamic process under DNA nick, indicating the influence of nick position on the relaxation of the supercoiled DNA.

DNA fluctuations reveal the size and dynamics of topological domains

DNA supercoiling is a key regulatory mechanism that orchestrates DNA readout, recombination, and genome maintenance. DNA-binding proteins often mediate these processes by bringing two distant DNA sites together, thereby inducing (transient) topological domains. In order to understand the dynamics and molecular architecture of protein-induced topological domains in DNA, quantitative and time-resolved approaches are required. Here, we present a methodology to determine the size and dynamics of topological domains in supercoiled DNA in real time and at the single-molecule level. Our approach is based on quantifying the extension fluctuations-in addition to the mean extension-of supercoiled DNA in magnetic tweezers (MT). Using a combination of high-speed MT experiments, Monte Carlo simulations, and analytical theory, we map out the dependence of DNA extension fluctuations as a function of supercoiling density and external force. We find that in the plectonemic regime, the extension variance increases linearly with increasing supercoiling density and show how this enables us to determine the formation and size of topological domains. In addition, we demonstrate how the transient (partial) dissociation of DNA-bridging proteins results in the dynamic sampling of different topological states, which allows us to deduce the torsional stiffness of the plectonemic state and the kinetics of protein-plectoneme interactions. We expect our results to further the understanding and optimization of magnetic tweezer measurements and to enable quantification of the dynamics and reaction pathways of DNA processing enzymes in the context of physiologically relevant forces and supercoiling densities.

Interaction of Proteins with Inverted Repeats and Cruciform Structures in Nucleic Acids

Cruciforms occur when inverted repeat sequences in double-stranded DNA adopt intra-strand hairpins on opposing strands. Biophysical and molecular studies of these structures confirm their characterization as four-way junctions and have demonstrated that several factors influence their stability, including overall chromatin structure and DNA supercoiling. Here, we review our understanding of processes that influence the formation and stability of cruciforms in genomes, covering the range of sequences shown to have biological significance. It is challenging to accurately sequence repetitive DNA sequences, but recent advances in sequencing methods have deepened understanding about the amounts of inverted repeats in genomes from all forms of life. We highlight that, in the majority of genomes, inverted repeats are present in higher numbers than is expected from a random occurrence. It is, therefore, becoming clear that inverted repeats play important roles in regulating many aspects of DNA metabolism, including replication, gene expression, and recombination. Cruciforms are targets for many architectural and regulatory proteins, including topoisomerases, p53, Rif1, and others. Notably, some of these proteins can induce the formation of cruciform structures when they bind to DNA. Inverted repeat sequences also influence the evolution of genomes, and growing evidence highlights their significance in several human diseases, suggesting that the inverted repeat sequences and/or DNA cruciforms could be useful therapeutic targets in some cases.

Genesis of Open States Zones in a DNA Molecule Depends on the Localization and Value of the Torque

The formation and dynamics of the open states in a double-stranded DNA molecule are largely determined by its mechanical parameters. The main one is the torque. However, the experimental study of DNA dynamics and the occurrence of open states is limited by the spatial resolution of available biophysical instruments. Therefore, in this work, on the basis of a mechanical mathematical model of DNA, calculations of the torque effect on the process of occurrence and dynamics of open states were carried out for the interferon alpha 17 gene. It was shown that torsion action leads to the occurrence of rotational movements of nitrogenous bases. This influence is nonlinear, and an increase in the amplitude of the torsion action does not lead to an automatic increase in the amplitude of rotational movements and an increase in the zones’ open states. Calculations with a constant torsion moment demonstrate that open states zones are more often formed at the boundaries of the gen and in regions with a predominance of A–T pairs. It is shown, that for the occurrence of open states in the part of the gene that contains a small number of A–T pairs, a large amount of torque is required. When the torque is applied to a certain region of the gene, the probability of the formation of the open state depends on the content of A–T pairs in this region, the size of this region, and on the exposure time. For this mathematical model, open states zones can be closed when the torsion action stops. The simulation results showed that the values of the torsion moment required for the appearance of open states zones, in some cases, are close to experimentally measured (13–15 pN·nm).

Angular Optical Trapping to Directly Measure DNA Torsional Mechanics

Angular optical trapping (AOT) is a powerful technique that permits direct angular manipulation of a trapped particle with simultaneous measurement of torque and rotation, while also retaining the capabilities of position and force detection. This technique provides unique approaches to investigate the torsional properties of nucleic acids and DNA-protein complexes, as well as impacts of torsional stress on fundamental biological processes, such as transcription and replication. Here we describe the principle, construction, and calibration of the AOT in detail and provide a guide to the performance of single-molecule torque measurements on DNA molecules. We include the constant-force method and, notably, a new constant-extension method that enables measurement of the twist persistence length of both extended DNA, under an extremely low force, and plectonemic DNA. This chapter can assist in the implementation and application of this technique for general researchers in the single-molecule field.

Torsional Stiffness of Extended and Plectonemic DNA

DNA torsional elastic properties play a crucial role in DNA structure, topology, and the regulation of motor protein progression. However, direct measurements of these parameters are experimentally challenging. Here, we present a constant-extension method integrated into an angular optical trap to directly measure torque during DNA supercoiling. We measured the twist persistence length of extended DNA to be 22 nm under an extremely low force (∼0.02  pN) and the twist persistence length of plectonemic DNA to be 24 nm. In addition, we implemented a rigorous data analysis scheme that bridged our measurements with existing theoretical models of DNA torsional behavior. This comprehensive set of torsional parameters demonstrates that at least 20% of DNA supercoiling is partitioned into twist for both extended DNA and plectonemic DNA. This work provides a new experimental methodology, as well as an analytical and interpretational framework, which will enable, expand, and enhance future studies of DNA torsional properties.

Ideas and methods of nonlinear mathematics and theoretical physics in DNA science: the McLaughlin-Scott equation and its application to study the DNA open state dynamics

The review is devoted to a new and rapidly developing area related to the application of ideas and methods of nonlinear mathematics and theoretical physics to study the internal dynamics of DNA and, in particular, the behavior of the open states of DNA. There are two main competing approaches to this research. The first approach is based on the molecular dynamics method, which takes into account the motions of all structural elements of the DNA molecule and all interactions between them. The second approach is based on prior selection of the main (dominant) motions and their mathematical description using a small number of model equations. This review describes the results of the study of the open states of DNA performed within the framework of the second approach using the McLaughlin-Scott equation. We present the results obtained both in the case of homogeneous sequences: poly (A), poly (T), poly (G) and poly (C), and in the inhomogeneous case when the McLaughlin-Scott equation has been used for studying the dynamics of open states activated in the promoters A1, A2 and A3 of the bacteriophage T7 genome, in the genes IFNA17, ADRB2, NOS1 and IL-5, in the pBR322 and pTTQ18 plasmids. Particular attention is paid to the results concerning the effect of various external fields on the behavior of open states. In the concluding part of the review, new possibilities and prospects for the development of the considered approach and especially of the McLaughlin-Scott equation are discussed.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s12551-021-00801-0.

Optical tweezers in single-molecule biophysics

Optical tweezers have become the method of choice in single-molecule manipulation studies. In this Primer, we first review the physical principles of optical tweezers and the characteristics that make them a powerful tool to investigate single molecules. We then introduce the modifications of the method to extend the measurement of forces and displacements to torques and angles, and to develop optical tweezers with single-molecule fluorescence detection capabilities. We discuss force and torque calibration of these instruments, their various modes of operation and most common experimental geometries. We describe the type of data obtained in each experimental design and their analyses. This description is followed by a survey of applications of these methods to the studies of protein-nucleic acid interactions, protein/RNA folding and molecular motors. We also discuss data reproducibility, the factors that lead to the data variability among different laboratories and the need to develop field standards. We cover the current limitations of the methods and possible ways to optimize instrument operation, data extraction and analysis, before suggesting likely areas of future growth.

Versatile Multilayer Metamaterial Nanoparticles with Tailored Optical Constants for Force and Torque Transduction

The ability to apply force and torque directly to micro- and nanoscale particles in optical traps has a wide range of applications. While full control of both force and torque in three dimensions has been realized using top-down fabrication of rod-shaped particles composed of birefringent crystalline materials, widespread usage of such particles is limited as the optical constants of the predominant birefringent materials (quartz SiO2 and rutile TiO2) preclude coverage of the full application space of optical trapping. Here, we show that multilayer metamaterial nanoparticles provide access to a wide range of optical constants that can be specifically tuned for each application. Selecting the material pair Nb2O5/SiO2 from the library of amorphous dielectrics as our metamaterial, we show that its refractive index and birefringence can be designed by adapting the ratio of layer thicknesses. Using a robust top-down fabrication process, we show that uniformly sized, free-floating Nb2O5/SiO2 particles with high birefringence at moderate refractive index are obtained at high yield. Using an optical torque wrench, we show that these particles function as joint force and torque transducers while maintaining excellent stability in aqueous solutions and can be controllably optimized for particular physical characteristics such as maximal torque transfer or rapid response time. We expect that such customizable birefringent metamaterial nanoparticles whose properties surpass those of conventional crystalline particles will provide a means to unleash the full potential of optical trapping applications.

R-Loop Physiology and Pathology: A Brief Review

Physiological and pathological roles for R-loop structures continue to be discovered, and studies suggest that R-loops could contribute to human disease. R-loops are nucleic acid structures characterized by a DNA:RNA hybrid and displaced single-stranded DNA that occur in connection with transcription. R-loops form naturally and have been shown to be important for a number of physiological processes such as mitochondrial replication initiation, class switch recombination, DNA repair, modulating DNA topology, and regulation of gene expression. However, subsets of R-loops or persistent R-loops lead to DNA breaks, chromosome rearrangement, and genome instability. In addition, R-loops have been linked to human diseases, specifically neurological disorders and cancer. Of the large amount of research produced recently on R-loops, this review covers evidence for R-loop involvement in normal cellular physiology and pathophysiology, as well as describing factors that contribute to R-loop regulation.

Dynamics of the Buckling Transition in Double-Stranded DNA and RNA

DNA under torsional strain undergoes a buckling transition that is the fundamental step in plectoneme nucleation and supercoil dynamics, which are critical for the processing of genomic information. Despite its importance, quantitative models of the buckling transition, in particular to also explain the surprising two-orders-of-magnitude difference between the buckling times for RNA and DNA revealed by single-molecule tweezers experiments, are currently lacking. Additionally, little is known about the configurations of the DNA during the buckling transition because they are not directly observable experimentally. Here, we use a discrete worm-like chain model and Brownian dynamics to simulate the DNA/RNA buckling transition. Our simulations are in good agreement with experimentally determined parameters of the buckling transition. The simulations show that the buckling time strongly and exponentially depends on the bending stiffness, which accounts for more than half the measured difference between DNA and RNA. Analyzing the microscopic conformations of the chain revealed by our simulations, we find clear evidence for a solenoid-shaped transition state and a curl intermediate. The curl intermediate features a single loop and becomes increasingly populated at low forces. Taken together, the simulations suggest that the worm-like chain model can account semiquantitatively for the buckling dynamics of both DNA and RNA.

Emerging roles for R-loop structures in the management of topological stress

R-loop structures are a prevalent class of alternative non-B DNA structures that form during transcription upon invasion of the DNA template by the nascent RNA. R-loops form universally in the genomes of organisms ranging from bacteriophages, bacteria, and yeasts to plants and animals, including mammals. A growing body of work has linked these structures to both physiological and pathological processes, in particular to genome instability. The rising interest in R-loops is placing new emphasis on understanding the fundamental physicochemical forces driving their formation and stability. Pioneering work in Escherichia coli revealed that DNA topology, in particular negative DNA superhelicity, plays a key role in driving R-loops. A clear role for DNA sequence was later uncovered. Here, we review and synthesize available evidence on the roles of DNA sequence and DNA topology in controlling R-loop formation and stability. Factoring in recent developments in R-loop modeling and single-molecule profiling, we propose a coherent model accounting for the interplay between DNA sequence and DNA topology in driving R-loop structure formation. This model reveals R-loops in a new light as powerful and reversible topological stress relievers, an insight that significantly expands the repertoire of R-loops' potential biological roles under both normal and aberrant conditions.

The Dissociation Rate of Acetylacetonate Ligands Governs the Size of Ferrimagnetic Zinc Ferrite Nanocubes

Magnetic nanoparticles are critical to a broad range of applications from medical diagnostics and therapeutics to biotechnological processes and single-molecule manipulation. To advance these applications, facile and robust routes to synthesize highly magnetic nanoparticles over a wide size range are needed. Here, we demonstrate that changing the degassing temperature of thermal decomposition of metal acetylacetonate precursors from 90 to 25 °C tunes the size of ferrimagnetic Zn_xFe_3-xO₄ nanocubes from 25 to 100 nm, respectively. We show that degassing at 90 °C nearly entirely removes acetylacetone ligands from the reaction, which results in an early formation of monomers and a reaction-controlled growth following LaMer's model toward small nanocubes. In contrast, degassing at 25 °C only partially dissociates acetylacetone ligands from the metal center and triggers a delayed formation of monomers, which leads to intermediate assembled structures made of tiny irregular crystallites and an eventual formation of large nanocubes via a diffusion-controlled growth mechanism. Using complementary techniques, we determine the substitution fraction x of Zn²⁺ to be in the range of 0.35-0.37. Our method reduces the complexity of the thermal decomposition method by narrowing the synthesis parameter space to a single physical parameter and enables fabrication of highly magnetic and uniform zinc ferrite nanocubes over a broad size range. The resulting particles are promising for a range of applications from magnetic fluid hyperthermia to actuation of macromolecules.

Intermediate states of molecular self-assembly from liquid-cell electron microscopy

Graphene liquid-cell electron microscopy reveals intermediate states of self-assembly—in this example, DNA when single strands form double helices. Molecules are observed for up to minutes at a time without apparent beam damage when electron energy and electron dose are low. Simultaneous in situ single-molecule imaging of conformational adaptations and motion gives more comprehensive understanding of self-assembly successes, failures, and error-producing mechanisms, confirming some earlier predictions and also presenting surprises. Loop intermediates were observed to facilitate error correction. Hybridization events accompany enhanced translational mobility and mechanistically specific persistent rotation. The information obtained goes beyond that from other single-molecule methods.

Traditional single-molecule methods do not report whole-molecule kinetic conformations, and their adaptive shape changes during the process of self-assembly. Here, using graphene liquid-cell electron microscopy with electrons of low energy at low dose, we show that this approach resolves the time dependence of conformational adaptations of macromolecules for times up to minutes, the resolution determined by motion blurring, with DNA as the test case. Single-stranded DNA molecules are observed in real time as they hybridize near the solid surface to form double-stranded helices; we contrast molecules the same length but differing in base-pair microstructure (random, blocky, and palindromic hairpin) whose key difference is that random sequences possess only one stable final state, but the others offer metastable intermediate structures. Hybridization is observed to couple with enhanced translational mobility and torsion-induced rotation of the molecule. Prevalent transient loops are observed in error-correction processes. Transient melting and other failed encounters are observed in the competitive binding of multiple single-stranded molecules. Among the intermediate states reported here, some were predicted but not observed previously, and the high incidence of looping and enhanced mobility come as surprises. The error-producing mechanisms, failed encounters, and transient intermediate states would not be easily resolved by traditional single-molecule methods. The methods generalize to visualize motions and interactions of other organic macromolecules.

Supercoiling DNA optically

Torsional stress plays a vital role in many genomic transactions, including replication and transcription, and often results in underwound (negatively supercoiled) DNA. Here, we present a single-molecule method, termed Optical DNA Supercoiling (ODS), that advances our ability to study negatively supercoiled DNA. Since ODS is based on dual-trap optical tweezers, it is compatible with a wide range of functionalities that are difficult to combine with traditional methods of DNA twist control. This includes the ability to image supercoiled DNA with fluorescence microscopy and move the supercoiled substrate rapidly between different buffer/protein solutions. We demonstrate that ODS yields unique and important insights into both the biomechanical properties of negatively supercoiled DNA and the dynamics of DNA–protein interactions on underwound DNA.

Cellular DNA is regularly subject to torsional stress during genomic processes, such as transcription and replication, resulting in a range of supercoiled DNA structures. For this reason, methods to prepare and study supercoiled DNA at the single-molecule level are widely used, including magnetic, angular-optical, micropipette, and magneto-optical tweezers. However, it is currently challenging to combine DNA supercoiling control with spatial manipulation and fluorescence microscopy. This limits the ability to study complex and dynamic interactions of supercoiled DNA. Here we present a single-molecule assay that can rapidly and controllably generate negatively supercoiled DNA using a standard dual-trap optical tweezers instrument. This method, termed Optical DNA Supercoiling (ODS), uniquely combines the ability to study supercoiled DNA using force spectroscopy, fluorescence imaging of the whole DNA, and rapid buffer exchange. The technique can be used to generate a wide range of supercoiled states, with between <5 and 70% lower helical twist than nonsupercoiled DNA. Highlighting the versatility of ODS, we reveal previously unobserved effects of ionic strength and sequence on the structural state of underwound DNA. Next, we demonstrate that ODS can be used to directly visualize and quantify protein dynamics on supercoiled DNA. We show that the diffusion of the mitochondrial transcription factor TFAM can be significantly hindered by local regions of underwound DNA. This finding suggests a mechanism by which supercoiling could regulate mitochondrial transcription in vivo. Taken together, we propose that ODS represents a powerful method to study both the biophysical properties and biological interactions of negatively supercoiled DNA.

High Trap Stiffness Microcylinders for Nanophotonic Trapping

Nanophotonic waveguides have enabled on-chip optical trap arrays for high-throughput manipulation and measurements. However, the realization of the full potential of these devices requires trapping enhancement for applications that need large trapping force. Here, we demonstrate a solution via fabrication of high refractive index cylindrical trapping particles. Using two different fabrication processes, a cleaving method and a novel lift-off method, we produced cylindrical silicon nitride (Si₃N₄) particles and characterized their trapping properties using the recently developed nanophotonic standing-wave array trap (nSWAT) platform. Relative to conventionally used polystyrene microspheres, the fabricated Si₃N₄ microcylinders attain an approximately 3- to 6-fold trap stiffness enhancement. Furthermore, both fabrication processes permit tunable microcylinder geometry, and the lift-off method also results in ultrasmooth surface termination of the ends of the microcylinders. These combined features make the Si₃N₄ microcylinders uniquely suited for a broad range of high-throughput, high-force, nanophotonic waveguide-based optical trapping applications.

A Tour de Force on the Double Helix: Exploiting DNA Mechanics To Study DNA-Based Molecular Machines

DNA is both a fundamental building block of life and a fascinating natural polymer. The advent of single-molecule manipulation tools made it possible to exert controlled force on individual DNA molecules and measure their mechanical response. Such investigations elucidated the elastic properties of DNA and revealed its distinctive structural configurations across force regimes. In the meantime, a detailed understanding of DNA mechanics laid the groundwork for single-molecule studies of DNA-binding proteins and DNA-processing enzymes that bend, stretch, and twist DNA. These studies shed new light on the metabolism and transactions of nucleic acids, which constitute a major part of the cell's operating system. Furthermore, the marriage of single-molecule fluorescence visualization and force manipulation has enabled researchers to directly correlate the applied tension to changes in the DNA structure and the behavior of DNA-templated complexes. Overall, experimental exploitation of DNA mechanics has been and will continue to be a unique and powerful strategy for understanding how molecular machineries recognize and modify the physical state of DNA to accomplish their biological functions.

Single-Crystal Rutile TiO2 Nanocylinders are Highly Effective Transducers of Optical Force and Torque

Optical trapping of (sub)micron-sized particles is broadly employed in nanoscience and engineering. The materials commonly employed for these particles, however, have physical properties that limit the transfer of linear or angular momentum (or both). This reduces the magnitude of forces and torques, and the spatiotemporal resolution, achievable in linear and angular traps. Here, we overcome these limitations through the use of single-crystal rutile TiO₂, which has an exceptionally large optical birefringence, a high index of refraction, good chemical stability, and is amenable to geometric control at the nanoscale. We show that rutile TiO₂ nanocylinders form powerful joint force and torque transducers in aqueous environments by using only moderate laser powers to apply nN·nm torques at kHz rotational frequencies to tightly trapped particles. In doing so, we demonstrate how rutile TiO₂ nanocylinders outperform other materials and offer unprecedented opportunities to expand the control of optical force and torque at the nanoscale.

Rescuing Replication from Barriers: Mechanistic Insights from Single-Molecule Studies

To prevent replication failure due to fork barriers, several mechanisms have evolved to restart arrested forks independent of the origin of replication. Our understanding of these mechanisms that underlie replication reactivation has been aided through unique dynamic perspectives offered by single-molecule techniques. These techniques, such as optical tweezers, magnetic tweezers, and fluorescence-based methods, allow researchers to monitor the unwinding of DNA by helicase, nucleotide incorporation during polymerase synthesis, and replication fork progression in real time. In addition, they offer the ability to distinguish DNA intermediates after obstacles to replication at high spatial and temporal resolutions, providing new insights into the replication reactivation mechanisms. These and other highlights of single-molecule techniques and remarkable studies on the recovery of the replication fork from barriers will be discussed in this review.

Rotating magnetic particles for lab-on-chip applications - a comprehensive review

Magnetic particles are widely used in lab-on-chip and biosensing applications, because they have a high surface-to-volume ratio, they can be actuated with magnetic fields and many biofunctionalization options are available. The most well-known actuation method is to apply a magnetic field gradient which generates a translational force on the particles and allows separation of the particles from a suspension. A more recently developed magnetic actuation method is to exert torque on magnetic particles by a rotating magnetic field. Rotational actuation can be achieved with a field that is uniform in space and it allows for a precise control of torque, orientation, and angular velocity of magnetic particles in lab-on-chip devices. A wide range of studies have been performed with rotating MPs, demonstrating fluid mixing, concentration determination of biological molecules in solution, and characterization of structure and function of biomolecules at the single-molecule level. In this paper we give a comprehensive review of the historical development of MP rotation studies, including configurations for field generation, physical model descriptions, and biological applications. We conclude by sketching the scientific and technological developments that can be expected in the future in the field of rotating magnetic particles for lab-on-chip applications.

Negative optical torque on a microsphere in optical tweezers

We show that the optical force field in optical tweezers with elliptically polarized beams has the opposite handedness for a wide range of particle sizes and for the most common configurations. Our method is based on the direct observation of the particle equilibrium position under the effect of a transverse Stokes drag force, and its rotation around the optical axis by the mechanical effect of the optical torque. We find overall agreement with theory, with no fitting, provided that astigmatism, which is characterized separately, is included in the theoretical description. Our work opens the way for characterization of the trapping parameters, such as the microsphere complex refractive index and the astigmatism of the optical system, from measurements of the microsphere rotation angle.

Transcription factor regulation of RNA polymerase's torque generation capacity

During transcription, RNA polymerase (RNAP) supercoils DNA as it translocates. The resulting torsional stress in DNA can accumulate and, in the absence of regulatory mechanisms, becomes a barrier to RNAP elongation, causing RNAP stalling, backtracking, and transcriptional arrest. Here we investigate whether and how a transcription factor may regulate both torque-induced Escherichia coli RNAP stalling and the torque generation capacity of RNAP. Using a unique real-time angular optical trapping assay, we found that RNAP working against a resisting torque was highly prone to extensive backtracking. We then investigated transcription in the presence of GreB, a transcription factor known to rescue RNAP from the backtracked state. We found that GreB greatly suppressed RNAP backtracking and remarkably increased the torque that RNAP was able to generate by 65%, from 11.2 pN⋅nm to 18.5 pN·nm. Variance analysis of the real-time positional trajectories of RNAP after a stall revealed the kinetic parameters of backtracking and GreB rescue. These results demonstrate that backtracking is the primary mechanism by which torsional stress limits transcription and that the transcription factor GreB effectively enhances the torsional capacity of RNAP. These findings suggest a broader role for transcription factors in regulating RNAP functionality and elongation.

Transfer-matrix calculations of the effects of tension and torque constraints on DNA-protein interactions

Organization and maintenance of the chromosomal DNA in living cells strongly depends on the DNA interactions with a plethora of DNA-binding proteins. Single-molecule studies show that formation of nucleoprotein complexes on DNA by such proteins is frequently subject to force and torque constraints applied to the DNA. Although the existing experimental techniques allow to exert these type of mechanical constraints on individual DNA biopolymers, their exact effects in regulation of DNA-protein interactions are still not completely understood due to the lack of systematic theoretical methods able to efficiently interpret complex experimental observations. To fill this gap, we have developed a general theoretical framework based on the transfer-matrix calculations that can be used to accurately describe behaviour of DNA-protein interactions under force and torque constraints. Potential applications of the constructed theoretical approach are demonstrated by predicting how these constraints affect the DNA-binding properties of different types of architectural proteins. Obtained results provide important insights into potential physiological functions of mechanical forces in the chromosomal DNA organization by architectural proteins as well as into single-DNA manipulation studies of DNA-protein interactions.

Controlled Mechanical Motions of Microparticles in Optical Tweezers

Optical tweezers, formed by a highly focused laser beam, have intriguing applications in biology and physics. Inspired by molecular rotors, numerous optical beams and artificial particles have been proposed to build optical tweezers trapping microparticles, and extensive experiences have been learned towards constructing precise, stable, flexible and controllable micromachines. The mechanism of interaction between particles and localized light fields is quite different for different types of particles, such as metal particles, dielectric particles and Janus particles. In this article, we present a comprehensive overview of the latest development on the fundamental and application of optical trapping. The emphasis is placed on controllable mechanical motions of particles, including rotation, translation and their mutual coupling under the optical forces and torques created by a wide variety of optical tweezers operating on different particles. Finally, we conclude by proposing promising directions for future research.

The influence of the DNA torque on the dynamics of transcription bubbles in plasmid PTTQ18

In this work, we study numerically the influence of the DNA torque on the movement of transcription bubbles in the potential field formed by the sequence of plasmid PTTQ18. To imitate the movement, we apply a modified sine-Gordon equation with the two additional terms that describe the effects of dissipation and the action of the DNA torsion torque, and with the coefficients that depend on the sequence of bases. We obtain the trajectories of the transcription bubbles and investigate the dependence of the trajectories on the initial bubble velocity and the DNA torsion torque. It is shown that not the initial bubble velocity but the DNA torsion torque governs the trajectories of the transcription bubbles.

Quantifying Local Molecular Tension Using Intercalated DNA Fluorescence

The ability to measure mechanics and forces in biological nanostructures, such as DNA, proteins and cells, is of great importance as a means to analyze biomolecular systems. However, current force detection methods often require specialized instrumentation. Here, we present a novel and versatile method to quantify tension in molecular systems locally and in real time, using intercalated DNA fluorescence. This approach can report forces over a range of at least ∼0.5-65 pN with a resolution of 1-3 pN, using commercially available intercalating dyes and a general-purpose fluorescence microscope. We demonstrate that the method can be easily implemented to report double-stranded (ds)DNA tension in any single-molecule assay that is compatible with fluorescence microscopy. This is particularly useful for multiplexed techniques, where measuring applied force in parallel is technically challenging. Moreover, tension measurements based on local dye binding offer the unique opportunity to determine how an applied force is distributed locally within biomolecular structures. Exploiting this, we apply our method to quantify the position-dependent force profile along the length of flow-stretched DNA and reveal that stretched and entwined DNA molecules-mimicking catenated DNA structures in vivo-display transient DNA-DNA interactions. The method reported here has obvious and broad applications for the study of DNA and DNA-protein interactions. Additionally, we propose that it could be employed to measure forces in any system to which dsDNA can be tethered, for applications including protein unfolding, chromosome mechanics, cell motility, and DNA nanomachines.

DNA Conformation Regulates Gene Expression: The MYC Promoter and Beyond

Emerging evidence suggests that DNA topology plays an instructive role in cell fate control through regulation of gene expression. Transcription produces torsional stress, and the resultant supercoiling of the DNA molecule generates an array of secondary structures. In turn, local DNA architecture is harnessed by the cell, acting within sensory feedback mechanisms to mediate transcriptional output. MYC is a potent oncogene, which is upregulated in the majority of cancers; thus numerous studies have focused on detailed understanding of its regulation. Dissection of regulatory regions within the MYC promoter provided the first hint that intimate feedback between DNA topology and associated DNA remodeling proteins is critical for moderating transcription. As evidence of such regulation is also found in the context of many other genes, here we expand on the prototypical example of the MYC promoter, and also explore DNA architecture in a genome-wide context as a global mechanism of transcriptional control.

Single-Molecule Angular Optical Trapping for Studying Transcription Under Torsion

Optical tweezers are flexible and powerful single-molecule tools that have been extensively utilized in biophysical studies. With their ability to stretch and twist DNA, and measure its force and torque simultaneously, they provide excellent opportunities to gain novel insights into the function of protein motors and protein-DNA interactions. Recently, a novel DNA supercoiling assay using an angular optical tweezers (AOT) has been developed to investigate torque generation during transcription. Here, we provide a detailed and practical guide to performing this technique. Using bacterial RNA polymerase (RNAP) as an example, we present protocols for constructing and calibrating an AOT instrument, preparing DNA templates, and acquiring and analyzing real-time data for transcription under DNA supercoiling. While these protocols were initially developed with E. coli RNAP, they can be readily adapted to study other DNA-based motor proteins.

Understanding the Relative Flexibility of RNA and DNA Duplexes: Stretching and Twist-Stretch Coupling

The flexibility of double-stranded (ds) RNA and dsDNA is crucial for their biological functions. Recent experiments have shown that the flexibility of dsRNA and dsDNA can be distinctively different in the aspects of stretching and twist-stretch coupling. Although various studies have been performed to understand the flexibility of dsRNA and dsDNA, there is still a lack of deep understanding of the distinctive differences in the flexibility of dsRNA and dsDNA helices as pertains to their stretching and twist-stretch coupling. In this work, we have explored the relative flexibility in stretching and twist-stretch coupling between dsRNA and dsDNA by all-atom molecular dynamics simulations. The calculated stretch modulus and twist-stretch coupling are in good accordance with the existing experiments. Our analyses show that the differences in stretching and twist-stretch coupling between dsRNA and dsDNA helices are mainly attributed to their different (A- and B-form) helical structures. Stronger basepair inclination and slide in dsRNA is responsible for the apparently weaker stretching rigidity versus that of dsDNA, and the opposite twist-stretch coupling for dsRNA and dsDNA is also attributed to the stronger basepair inclination in dsRNA than in dsDNA. Our calculated macroscopic elastic parameters and microscopic analyses are tested and validated by different force fields for both dsRNA and dsDNA.

Single-molecule spectroelectrochemical cross-correlation during redox cycling in recessed dual ring electrode zero-mode waveguides

The ability of zero-mode waveguides (ZMW) to guide light into subwavelength-diameter nanoapertures has been exploited for studying electron transfer dynamics in zeptoliter-volume nanopores under single-molecule occupancy conditions. In this work, we report the spectroelectrochemical detection of individual molecules of the redox-active, fluorogenic molecule flavin mononucleotide (FMN) freely diffusing in solution. Our approach is based on an array of nanopore-confined recessed dual ring electrodes, wherein repeated reduction and oxidation of a single molecule at two closely spaced annular working electrodes yields amplified electrochemical signals. We have articulated these structures with an optically transparent bottom, so that the nanopores are bifunctional, exhibiting both nanophotonic and nanoelectrochemical behaviors allowing the coupling between electron transfer and fluorescence dynamics to be studied under redox cycling conditions. We also investigated the electric field intensity in electrochemical ZMWs (E-ZMW) through finite-element simulations, and the amplification of fluorescence by redox cycling agrees well with predictions based on optical confinement effects inside the E-ZMW. Proof-of-principle experiments are conducted showing that electrochemical and fluorescence signals may be correlated to reveal single molecule fluctuations in the array population. Cross-correlation of single molecule fluctuations in amperometric response and single photon emission provides unequivocal evidence of single molecule sensitivity.

Tweezing of Magnetic and Non-Magnetic Objects with Magnetic Fields

Although strong magnetic fields cannot be conveniently "focused" like light, modern microfabrication techniques enable preparation of microstructures with which the field gradients - and resulting magnetic forces - can be localized to very small dimensions. This ability provides the foundation for magnetic tweezers which in their classical variant can address magnetic targets. More recently, the so-called negative magnetophoretic tweezers have also been developed which enable trapping and manipulations of completely nonmagnetic particles provided that they are suspended in a high-magnetic-susceptibility liquid. These two modes of magnetic tweezing are complimentary techniques tailorable for different types of applications. This Progress Report provides the theoretical basis for both modalities and illustrates their specific uses ranging from the manipulation of colloids in 2D and 3D, to trapping of living cells, control of cell function, experiments with single molecules, and more.

Tunable nanophotonic array traps with enhanced force and stability

A nanophotonic trapping platform based on on-chip tunable optical interference allows parallel processing of biomolecules and holds promise to make single molecule manipulation and precision measurements more easily and broadly available. The nanophotonic standing wave array trap (nSWAT) device [Nat. Nanotechnol. 9, 448 (2014); Nano Lett. 16, 6661 (2016)] represents such a platform and can trap a large array of beads by the evanescent field of the standing wave of a nanophotonic waveguide and reposition them using an integrated microheater. In this paper, by taking a systematic design approach, we present a new generation of nSWAT devices with significant enhancement of the optical trapping force, stiffness, and stability, while the quality of the standing wave trap is resistant to fabrication imperfections. The device is implemented on a silicon nitride photonic platform and operates at 1064 nm wavelength which permits low optical absorption by the aqueous solution. Such performance improvements open a broader range of applications based on these on-chip optical traps.

Optical Torque Wrench Design and Calibration

Expanding the capabilities of optical traps with angular control of the trapped particle has numerous potential applications in all fields where standard linear optical tweezers are employed. Here we describe in detail the construction, alignment, and calibration of the Optical Torque Wrench, a mode of function that can be added to linear optical tweezers to simultaneously apply and measure both force and torque on birefringent microscopic cylindrical particles. The interaction between the linear polarization of the laser and the birefringent cylinder creates an angular trap for the particle orientation, described by a periodic potential. As a consequence of the experimental control of the tilt of the periodic potential, the dynamical excitability of the system can be observed. Angular optical tweezers remain less widespread than their linear counterpart. We hope this technical guide can foster their development and new applications.

The dynamic interplay between DNA topoisomerases and DNA topology

Topological properties of DNA influence its structure and biochemical interactions. Within the cell, DNA topology is constantly in flux. Transcription and other essential processes, including DNA replication and repair, not only alter the topology of the genome but also introduce additional complications associated with DNA knotting and catenation. These topological perturbations are counteracted by the action of topoisomerases, a specialized class of highly conserved and essential enzymes that actively regulate the topological state of the genome. This dynamic interplay among DNA topology, DNA processing enzymes, and DNA topoisomerases is a pervasive factor that influences DNA metabolism in vivo. Building on the extensive structural and biochemical characterization over the past four decades that has established the fundamental mechanistic basis of topoisomerase activity, scientists have begun to explore the unique roles played by DNA topology in modulating and influencing the activity of topoisomerases. In this review we survey established and emerging DNA topology-dependent protein-DNA interactions with a focus on in vitro measurements of the dynamic interplay between DNA topology and topoisomerase activity.

Electromagnetic tweezers with independent force and torque control

Magnetic tweezers are powerful tools to manipulate and study the mechanical properties of biological molecules and living cells. In this paper we present a novel, bona fide electromagnetic tweezer (EMT) setup that allows independent control of the force and torque applied via micrometer-sized magnetic beads to a molecule under study. We implemented this EMT by combining a single solenoid that generates force (f-EMT) with a set of four solenoids arranged into a symmetric quadrupole to generate torque (τ-EMT). To demonstrate the capability of the tweezers, we attached optically asymmetric Janus beads to single, tethered DNA molecules. We show that tension in the piconewton force range can be applied to single DNA molecules and the molecule can simultaneously be twisted with torques in the piconewton-nanometer range. Furthermore, the EMT allows the two components to be independently controlled. At various force levels applied to the Janus bead, the trap torsional stiffness can be continuously changed simply by varying the current magnitude applied to the τ-EMT. The flexible and independent control of force and torque by the EMT makes it an ideal tool for a range of measurements where tensional and torsional properties need to be studied simultaneously on a molecular or cellular level.

DNA supercoiling during transcription

The twin-supercoiled-domain model describes how transcription can drive DNA supercoiling, and how DNA supercoiling, in turn plays an important role in regulating gene transcription. In vivo and in vitro experiments have disclosed many details of the complex interactions in this relationship, and recently new insights have been gained with the help of genome-wide DNA supercoiling mapping techniques and single molecule methods. This review summarizes the general mechanisms of the interplay between DNA supercoiling and transcription, considers the biological implications, and focuses on recent important discoveries and technical advances in this field. We highlight the significant impact of DNA supercoiling in transcription, but also more broadly in all processes operating on DNA.

The Dynamic Interplay Between DNA Topoisomerases and DNA Topology

Topological properties of DNA influence its structure and biochemical interactions. Within the cell DNA topology is constantly in flux. Transcription and other essential processes including DNA replication and repair, alter the topology of the genome, while introducing additional complications associated with DNA knotting and catenation. These topological perturbations are counteracted by the action of topoisomerases, a specialized class of highly conserved and essential enzymes that actively regulate the topological state of the genome. This dynamic interplay among DNA topology, DNA processing enzymes, and DNA topoisomerases, is a pervasive factor that influences DNA metabolism in vivo. Building on the extensive structural and biochemical characterization over the past four decades that established the fundamental mechanistic basis of topoisomerase activity, the unique roles played by DNA topology in modulating and influencing the activity of topoisomerases have begun to be explored. In this review we survey established and emerging DNA topology dependent protein-DNA interactions with a focus on in vitro measurements of the dynamic interplay between DNA topology and topoisomerase activity.

Probing the mechanical properties, conformational changes, and interactions of nucleic acids with magnetic tweezers

Nucleic acids are central to the storage and transmission of genetic information. Mechanical properties, along with their sequence, both enable and fundamentally constrain the biological functions of DNA and RNA. For small deformations from the equilibrium conformations, nucleic acids are well described by an isotropic elastic rod model. However, external forces and torsional strains can induce conformational changes, giving rise to a complex force-torque phase diagram. This review focuses on magnetic tweezers as a powerful tool to precisely determine both the elastic parameters and conformational transitions of nucleic acids under external forces and torques at the single-molecule level. We review several variations of magnetic tweezers, in particular conventional magnetic tweezers, freely orbiting magnetic tweezers and magnetic torque tweezers, and discuss their characteristic capabilities. We then describe the elastic rod model for DNA and RNA and discuss conformational changes induced by mechanical stress. The focus lies on the responses to torque and twist, which are crucial in the mechanics and interactions of nucleic acids and can directly be measured using magnetic tweezers. We conclude by highlighting several recent studies of nucleic acid-protein and nucleic acid-small-molecule interactions as further applications of magnetic tweezers and give an outlook of some exciting developments to come.

Unravelling the structural plasticity of stretched DNA under torsional constraint

Regions of the genome are often held under torsional constraint. Nevertheless, the influence of such constraint on DNA-protein interactions during genome metabolism is still poorly understood. Here using a combined optical tweezers and fluorescence microscope, we quantify and explain how torsional constraint influences the structural stability of DNA under applied tension. We provide direct evidence that concomitant basepair melting and helical unwinding can occur in torsionally constrained DNA at forces >∼50 pN. This striking result indicates that local changes in linking number can be absorbed by the rest of the DNA duplex. We also present compelling new evidence that an overwound DNA structure (likely P-DNA) is created (alongside underwound structures) at forces >∼110 pN. These findings substantiate previous theoretical predictions and highlight a remarkable structural plasticity of torsionally constrained DNA. Such plasticity may be required in vivo to absorb local changes in linking number in DNA held under torsional constraint.

Single-molecule portrait of DNA and RNA double helices

The composition and geometry of the genetic information carriers were described as double-stranded right helices sixty years ago. The flexibility of their sugar-phosphate backbones and the chemistry of their nucleotide subunits, which give rise to the RNA and DNA polymers, were soon reported to generate two main structural duplex states with biological relevance: the so-called A and B forms. Double-stranded (ds) RNA adopts the former whereas dsDNA is stable in the latter. The presence of flexural and torsional stresses in combination with environmental conditions in the cell or in the event of specific sequences in the genome can, however, stabilize other conformations. Single-molecule manipulation, besides affording the investigation of the elastic response of these polymers, can test the stability of their structural states and transition models. This approach is uniquely suited to understanding the basic features of protein binding molecules, the dynamics of molecular motors and to shedding more light on the biological relevance of the information blocks of life. Here, we provide a comprehensive single-molecule analysis of DNA and RNA double helices in the context of their structural polymorphism to set a rigorous interpretation of their material response both inside and outside the cell. From early knowledge of static structures to current dynamic investigations, we review their phase transitions and mechanochemical behaviour and harness this fundamental knowledge not only through biological sciences, but also for Nanotechnology and Nanomedicine.

Nanomechanical force transducers for biomolecular and intracellular measurements: is there room to shrink and why do it?

Over the past couple of decades there has been a tremendous amount of progress on the development of ultrasensitive nanomechanical instruments, which has enabled scientists to peer for the first time into the mechanical world of biomolecular systems. Currently, work-horse instruments such as the atomic force microscope and optical/magnetic tweezers have provided the resolution necessary to extract quantitative force data from various molecular systems down to the femtonewton range, but it remains difficult to access the intracellular environment with these analytical tools as they have fairly large sizes and complicated feedback systems. This review is focused on highlighting some of the major milestones and discoveries in the field of biomolecular mechanics that have been made possible by the development of advanced atomic force microscope and tweezer techniques as well as on introducing emerging state-of-the-art nanomechanical force transducers that are addressing the size limitations presented by these standard tools. We will first briefly cover the basic setup and operation of these instruments, and then focus heavily on summarizing advances in in vitro force studies at both the molecular and cellular level. The last part of this review will include strategies for shrinking down the size of force transducers and provide insight into why this may be important for gaining a more complete understanding of cellular activity and function.